A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

The calculator is used to solve certain formidable equations, which arise naturally and which may be difficult or impossible to solve by standard methods, by a method of successive approximations. (MP)

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)

Teaching which does not in any significant way address the genesis of mathematical ideas hides the fact that mathematics is created by people; that it involves intuition, exploring, conjecturing, and reasoning; and that it is purposeful. Such teaching can give students appearance that much of mathematics is very arbitrary; it just falls from the…

It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats the cognitive demand of a problem changes. The main objective of this study…

Presents compact algorithms, suitable for use with hand held calculators, for the calculation of potentiometric titration curves. (SL)

Presents an exact equation for calculating the volume of titrant as a function of the hydrogen ion concentration suitable for calculation on a hand held calculator. (SL)

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

Evaluates an instructional method in general chemistry that attempts to bridge the gap between algorithmic problem-solving abilities and conceptual understanding of chemistry students and emphasizes conceptual problem solving in the initial phase of a concept. Concludes that using a conceptual focus for the chemistry courses had many positive…

Two randomized trials were conducted to determine (1) whether the use of the algorithm system has a measurable effect on the clinical problem-solving behavior of physician's assistants, and (2) if so, which components of the algorithm system account for the effect. Inconclusive findings are reported. (LBH)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

Computer science education for the liberal arts student has both a practical value (creating an intelligent consumer) and an appreciative value (teaching algorithmic thinking). A computer literacy course can be structured to harmonize with the aims of liberal education. (SK)

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…